First of all thanks to both of you for your help.

You are correct there should be an i there where ProveIt said.

Accutually I have to solve this in three different ways.

By simplifying a+bi

by rewritting it in polar form

By using (as tonio did) Eulers approach.

Also this has to be done without a calculator, (that probably means that the argument rational).

Anyway the issue is that I donīt understand what I do wrong with the polar form thing: I just took the arguments in the denominator that gave me:

then the arguments in the nominator:

This is already a mess: in a fraction the upper part is called NUMERATOR and the lower one DENOMINATOR. Now, in the numerator you have , and in the denominator you have . Now you do the maths with the powers and you'll get , indeed. Tonio
and then substracted that gave me

but the correct answer is

not sure what Iīm doing wrong here...